On path energy of graphs

Saieed Akbari, Amir Hossein Ghodrati, Ivan Gutman, Mohammad Ali Hosseinzadeh, Elena V. Konstantinova

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

For a graph G with vertex set {v1, . . ., v n }, let P(G) be an n × n matrix whose (i, j)-entry is the maximum number of internally disjoint viv j -paths in G, if i ≠ j, and zero otherwise. The sum of absolute values of the eigenvalues of P(G) is called the path energy of G, denoted by PE. We prove that PE of a connected graph G of order n is at least 2(n− 1) and equality holds if and only if G is a tree. Also, we determine PE of a unicyclic graph of order n and girth k, showing that for every n, PE is an increasing function of k. Therefore, among unicyclic graphs of order n, the maximum and minimum PE-values are for k = n and k = 3, respectively. These results give affirmative answers to some conjectures proposed in MATCH.

Original languageEnglish
Pages (from-to)465-470
Number of pages6
JournalMatch
Volume81
Issue number2
Publication statusPublished - 1 Jan 2019

OECD FOS+WOS

  • 1.04 CHEMICAL SCIENCES
  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

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